Homeclass 10MathsProbabilityCompound Event

Compound Event

A compound event in probability is an event that contains more than one outcome from the sample space of a random experiment. Unlike an elementary event which has only a single outcome, a compound event is formed by combining two or more elementary events.

Key Concepts

A compound event represents a collection of multiple favorable outcomes that satisfy a specific condition.
It can occur in a single trial, such as rolling an even number on one die, or across multiple trials, such as getting two heads when tossing two coins.
The probability of a compound event is calculated by adding the probabilities of all the individual elementary events that make up the compound event.

Formula & Equation

P(E)=Number of outcomes favorable to ETotal number of possible outcomesP(E) = \frac{\text{Number of outcomes favorable to } E}{\text{Total number of possible outcomes}}

P(E) represents the probability of the compound event E.

Still confused about Compound Event?

Don't just read. Talk to our AI Teacher by voice, interrupt anytime, and clear your doubts instantly like a real classroom.

Download

Common Misconceptions

Myth: Compound events only occur when you perform multiple experiments at the same time, like rolling two dice or tossing three coins.
Fact: A compound event can happen in a single experiment. For example, rolling a number greater than 4 on a single die is a compound event because it includes two distinct outcomes (5 and 6).

Real World Applications

Rolling a standard six-sided die and getting a prime number. The favorable outcomes are 2, 3, and 5, making it a compound event.
Drawing a face card from a standard deck of 52 playing cards, which consists of 12 different favorable outcomes (Jacks, Queens, and Kings).

Frequently Asked Questions

What is the difference between an elementary event and a compound event?
An elementary event has exactly one outcome, like rolling a 3 on a die. A compound event has more than one outcome, like rolling an odd number.
How do you find the probability of a compound event?
You calculate it by dividing the total number of favorable outcomes that make up the compound event by the total number of possible outcomes in the sample space.

Keep Learning

Elementary EventEventSample Space